Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology

Universal behavior in fragmenting brittle, isotropic solids across material properties

A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a model is proposed which includes breakable two- and three-body particle interactions to calibrate elastic moduli and mode I and mode II fracture toughnesses. In the quasistatic limit, fragmentation leads to a power-law distribution of grain sizes which is truncated at a maximum grain mass that grows as a nontrivial power of system size. In the high-rate limit, truncation occurs at a mass that decreases as a power of increasing rate. A scaling description is used to characterize this behavior by collapsing the mean-square grain mass across rates and system sizes. Consistent scaling persists across all material properties studied, although there are differences in the evolution of grain size distributions with strain as the initial number of grains at fracture and their subsequent rate of production depend on Poisson's ratio. This evolving granular structure is found to induce a unique rheology where the ratio of the shear stress to pressure, an internal friction coefficient, decays approximately as the logarithm of increasing strain rate. The stress ratio also decreases at all rates with increasing strain as fragmentation progresses and depends on elastic properties of the solid.

Flow and arrest in stressed granular materials

Flowing granular materials often abruptly arrest if not driven by sufficient applied stresses. Such abrupt cessation of motion can be economically expensive in industrial materials handling and processing, and is significantly consequential in intermittent geophysical phenomena such as landslides and earthquakes. Using discrete element simulations, we calculate states of steady flow and arrest for granular materials under the conditions of constant applied pressure and shear stress, which are also most relevant in practice. Here the material can dilate or compact, and flow or arrest, in response to the applied stress. Our simulations highlight that under external stress, the intrinsic response of granular materials is characterized by uniquely-defined steady states of flow or arrest, which are highly sensitive to interparticle friction. While the flowing states can be equivalently characterized by volume fraction, coordination number or internal stress ratio, to characterize the states of shear arrest, one needs to also consider the structural anisotropy in the contact network. We highlight the role of dilation in the flow-arrest transition, and discuss our findings in the context of rheological transitions in granular materials.